1988 AMC 12 Problem 18
Attempt Problem 18 of the 1988 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1988 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
At the end of a professional bowling tournament, the top bowlers have a play-off. First # bowls # The loser receives th prize and the winner bowls # in another game. The loser of this game receives th prize and the winner bowls # The loser of this game receives rd prize and the winner bowls # The winner of this game gets st prize and the loser gets nd prize. In how many orders can bowlers # through # receive the prizes?
none of these
Answer: B
Small hint:
Exactly four games are played
Big hint:
Each sequence of winners determines a different prize order
Solution:
Each of the four games has two possible winners. A sequence of four outcomes uniquely determines the five prize positions, so there are orders.
Thus the correct answer is B.
Problem 18 in other years
- 1950 AMC 12
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